If 5^11 = 5^2 x 5m, what is the value of m?

The general solution to the differential equation is, |3x^4/(y(x+y))|x + |x^3| ln|y| + |x^3| ln|x+y| + h(x) = C.

The partial derivative of (3xy + y^2) with respect to y is 6xy + 2y, and the partial derivative of (x^2 + xy) with respect to x is 2x + y. Since these are not equal, the differential equation is not exact.

To make it exact, we need to find an integrating factor μ(x, y) such that μ(x, y)(3xy + y^2) dx + μ(x, y)(x^2 + xy) dy = 0 is exact. We can find μ(x, y) by using the formula:

μ(x, y) = e^(∫(∂M/∂y - ∂N/∂x)/N dx)

where M = 3xy + y^2 and N = x^2 + xy. We have:

(∂M/∂y - ∂N/∂x)/N = (6xy + 2y - 2x - y)/(x^2 + xy) = (6xy - x - y)/(x^2 + xy)

We can now find the integrating factor μ(x, y) by integrating this expression with respect to x:

μ(x, y) = e^(∫(6xy - x - y)/(x^2 + xy) dx) = e^(3ln|x| - ln|y| - ln|x+y| + C) = e^(ln|x^3/(y(x+y))| + C) = |x^3/(y(x+y))|e^C

where C is the constant of integration.

Now we multiply the original differential equation by the integrating factor μ(x, y) to obtain:

|3x^4/(y(x+y))| dx + |x^3/(y(x+y))| dy = 0

This is now an exact differential equation, and we can find its solution by integrating with respect to x or y. Integrating with respect to x, we get:

|3x^4/(y(x+y))|x + g(y) = C

where g(y) is the constant of integration. To find g(y), we integrate the coefficient of dy:

g(y) = ∫|x^3/(y(x+y))| dy = |x^3| ln|y| + |x^3| ln|x+y| + h(x)

where h(x) is another constant of integration. Substituting g(y) back into the solution, we have:

|3x^4/(y(x+y))|x + |x^3| ln|y| + |x^3| ln|x+y| + h(x) = C

This is the general solution to the differential equation.

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Answer:

When multiplying fractions, you first start with the two fractions you want to multiply. You multiply the numerators (the top numbers) together, and then multiply the denominators (the bottom numbers) together.

Answer:

Sum of all the exterior angles in any polygon is always 360º

Find the number of sides:

One exterior angles = 20º

Number of sides = 360 ÷ 20

Number of sides = 18

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) external angles is also known as exterior angles

exterior angle = 360

we have n=20

360/n=360/20=18

the external angles of a regular polygon of 20 is 18 degree

b) internal angles is also known as interior angles

interior angle = 180

exterior angle = 18

interior angle - exterior angle

180-18=162 degree

the internal angles of 20 is 162 degree

Answer:

0.6*45=27

Step-by-step explanation:

You have to change 60 percent into a decimal and multiply it by 45 because there are 45 questions and you wil get 27

Answer:

75 cents per can

Step-by-step explanation:

8 for $6 = 75 cents per can

10 for $10 = $1 per can

2 for $3 = $1.50 per can

The last store sold 28-oz for $1.40 each

To obtain the cost per 15-oz can of baked beans

28-oz / 15-oz = 1.86667of 15 - oz cans of baked beans can be obtained from 28 - oz.

The price per can will now be :

$1.40 / 1.8666666

= $0.75

= 0.75 * 100 = 75 cents

Hence, for the last store, they sold at 75 cents per can similar to the first store.

Answer:

75

Step-by-step explanation:

it is

Under the unbiased expectations theory of the term structure of interest rates, the expected one-year interest rate one year from now, E(2r1), is 10%.

The unbiased expectations theory states that the expected future rate (E(2r1)) is equal to the current rate (1R2). Therefore, the expected one-year interest rate one year from now, E(2r1), is 10%.

The unbiased expectations theory is a principle in finance that states that the expected future rate of return (E(2r1)) is equal to the current rate of return (r2). This theory suggests that market participants have rational expectations and their expectations are reflected in the current market prices. In other words, the theory posits that the current market prices incorporate all available information and reflect the best prediction of future prices.

In the example given, if the expected one-year interest rate one year from now is 10%, it means that market participants believe that the one-year interest rate in the future will be 10%. This expectation is reflected in the current market prices and is incorporated into the current rate of return.

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Answer:

8(1-2y)

Step-by-step explanation:

grouping like terms

Answer:

8 (1 - 2 y)

Step-by-step explanation:

Simplify the following:

-2 x - 4 + 2 (-3 y + x) - 2 (5 y - 6)

2 (-3 y + x) = -6 y + 2 x:

-2 x - 4 + -6 y + 2 x - 2 (5 y - 6)

-2 (5 y - 6) = 12 - 10 y:

-2 x - 4 + 2 x - 6 y + 12 - 10 y

Grouping like terms, -6 y - 10 y + 2 x - 2 x - 4 + 12 = (-6 y - 10 y) + (-2 x + 2 x) + (-4 + 12):

(-6 y - 10 y) + (-2 x + 2 x) + (-4 + 12)

-6 y - 10 y = -16 y:

-16 y + (12 - 4) + (2 x - 2 x)

12 - 4 = 8:

-16 y + 8 + (2 x - 2 x)

2 x - 2 x = 0:

8 - 16 y

Factor 8 out of 8 - 16 y:

Answer: 8 (1 - 2 y)

Step-by-step explanation:

Calculate the approximate value: 26 x 0.87462

Calculate: 22.74012

Round  22.74012 to the required place

Answer:22.7

Hope this helps

Answer: 1 is 50 and 2 is 70

Step-by-step explanation: these are both congruent and they are supplementary triangles

Because the triangles are just translated meaning they are moved and they are supplementary meaning they add up to 180° so we can subtract 180-70-60 to get 50 and the equation of triangle XYZ is 180-60-50 to get 70 those are the answers hope this helps :)

Answer: X=11

Step-by-step explanation:

                                     7x+ 13 = 90

                                                          (bring like terms together)

                                      7x=90-13

                                      7x=77

                                           therefore x= 11

HOPE THIS HELPS YOU....

AND MARK THE BRAINLIEST

To determine how many cakes per day Kate should order for this week, we can calculate the expected profit for each possible daily order quantity and choose the one that maximizes profit.

(a) Here are the steps:
1. Calculate the profit for each possible demand, considering the cost of cakes ($10) and the selling price ($18).
2. Multiply the profit by the probability of each demand level.
3. Sum up the expected profits for all demand levels. Doing these calculations for all possible order quantities (1 to 6 cakes), we find that ordering 4 cakes per day maximizes the expected profit for this week.
(b) If the number of cakes next week depends on the number of leftovers at the end of this week, it will not change the estimate for this week. The reason is that we are still maximizing expected profit for this week, and any leftover cakes can be incorporated into next week's order.
(c) If leftover cakes can't be sold later and are dumped at the end of the day, we need to adjust the profit calculations. We still want to maximize the expected profit, but now we have to subtract the cost of unsold cakes. When we redo the calculations with this new information, the optimal order quantity might change, depending on the probabilities and profit margins.
(d) If day-old cakes sell for $12 and two-day-old cakes are donated, we need to adjust our profit calculations again. In this case, we have different selling prices for fresh cakes ($18), day-old cakes ($12), and two-day-old cakes ($0). Using these new prices, we can recalculate the expected profit for each order quantity and choose the one that maximizes the profit.

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a. Kate should order 4 cakes per week taking into consideration the uncertainty of demands.

b. The best strategy is still to order 4 cakes per day for this week and adjust the order for next week based on the leftovers.

c. Kate should order 3 cakes per day for this week to minimize waste.

d. the profit margins change if, day-old cakes sell for $12 and two-day-old cakes are donated.

a. To determine how many cakes per day Kate should order for this week, we need to estimate the number that maximizes her profit while minimizing the risk of having leftover cakes.

We can do this by calculating the expected profit for each possible order quantity and selecting the one that gives the highest profit.
We can calculate the number of cakes by following the steps
1. Multiply the daily demand by its probability, then sum these products to get the expected daily demand:

(1 * .1) + (2 * .2) + (3 * .25) + (4 * .25) + (5 * .15) + (6 * .05) = 3.4 cakes
2. Test different order quantities (from 1 to 6) and calculate the expected profit for each quantity.
3. Select the order quantity with the highest expected profit.

For this problem, Kate should order 4 cakes per day for this week.

b. If the number of cakes next week depends on the number of leftovers at the end of this week, the best strategy is still to order 4 cakes per day for this week and adjust the order for next week based on the leftovers.

c. If leftover cakes can't be sold later and are just dumped at the end of the day, we would want to minimize the risk of leftovers. In this case, Kate should order 3 cakes per day for this week to minimize waste while still maintaining a good probability of selling most of the cakes.

d. If day-old cakes sell for $12 and two-day-old cakes are donated, the profit margins change, and the expected profit calculation should be updated accordingly.

After recalculating, Kate should still order 4 cakes per day for this week, as the order quantity provides the highest expected profit with this new pricing structure.

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Answer: 168 liters

Step-by-step explanation:

From the information given , we are informed that they put out 12 three-and-a-half liter containers and that each of these containers was filled four times during the storm.

The amount of rain that was collected in all goes thus:

Since each container was filled 4 times, the amount filled by each container will be:

= 3 1/2 liters × 4

= 14 liters

Therefore, the total amount for the 12 containers will be:

= 12 × 14 liters

= 168 liters

Answer:

the third box

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Reflect X axis is when the X value doesn't change, but the y value turns negative.

Reflect Y axis is when the Y value doesn't change, but the x value turns negative.

Here the point is (-11,-7)

Reflect X is (-11,7)

Reflect Y is (11,7)

To solve this problem, we can use the concept of similar triangles and the volume formula for a cone.The water level is rising at a rate of 4m/min when the water is 8m deep.

Given that the container is a right circular cone with a radius of 4m and a height of 16m, we can use the following volume formula for a cone:

V = (1/3) * π * r^2 * h

Where V is the volume, π is a constant (approximately 3.14), r is the radius, and h is the height.

To find how fast the water level is rising, we need to determine the rate of change of the volume with respect to time. We are given that the water is poured into the container at a constant rate of 16m^3/min.

Differentiating the volume formula with respect to time (t), we get:

dV/dt = (1/3) * π * (2r * dr/dt) * h + (1/3) * π * r^2 * dh/dt

Since we are interested in the rate of change of the water level, we can substitute the given values into the formula. When the water is 8m deep, the radius of the water surface can be found using similar triangles:

r/h = 4/16

Simplifying this gives:

r = (4/16) * h = h/4

Substituting these values into the volume formula and differentiating, we get: dV/dt = (1/3) * π * (2(h/4) * dh/dt) * h + (1/3) * π * (h/4)^2 * dh/dt

Simplifying further:

dV/dt = (1/3) * π * (h/2) * dh/dt + (1/48) * π * h^2 * dh/dt

Now, we know that dV/dt = 16m^3/min (the constant rate at which water is poured into the container). Let's plug this in and solve for dh/dt:

16 = (1/3) * π * (h/2) * dh/dt + (1/48) * π * h^2 * dh/dt

Multiplying through by 48/π and simplifying:

48 * 16 = 16 * h * dh/dt + h^2 * dh/dt

768 = 16h * dh/dt + h^2 * dh/dt

Factoring out dh/dt:

dh/dt * (16h + h^2) = 768

Now we need to find the value of h when the water is 8m deep. Plugging in h = 8 into the equation:

dh/dt * (16(8) + 8^2) = 768

dh/dt * (128 + 64) = 768

dh/dt * 192 = 768

dh/dt = 768/192

dh/dt = 4

Therefore, the water level is rising at a rate of 4m/min when the water is 8m deep.

Note: The units used in the calculations were meters and minutes, but it's important to check and ensure that the units are consistent throughout the problem.

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Answer:

A = 2299

Step-by-step explanation:

The figure is composed of:

one 55X33 rectangle and

one 22X22 square

Area of the shape:

\(a= (55)(33)+(22)^{2} =1815+484=2299\)

Hope this helps

Given, A = 21   B = 921

a. The given information is Mean = (10 + B) = (10 + 921) = 931

Standard Deviation = σ = 8

Sample size = n = 36

Confidence level = 95%

The formula for the confidence interval of the population mean is:

CI = X ± z(σ/√n)

Where X is the sample mean. z is the z-valueσ is the standard deviation n is the sample size We need to find the confidence interval of the population mean at 95% confidence level.

Hence, the confidence interval of the population mean is

CI = X ± z(σ/√n) = 931 ± 1.96(8/√36) = 931 ± 2.66

Therefore, the 95% confidence interval of the population mean is (928.34, 933.66).

b. The given information is the Sample size, n = (7 + A) = (7 + 21) = 28

Standard deviation, σ = 8

Confidence level = 90%

We need to find the 90% confidence interval for the variance.

For that, we use the Chi-Square distribution, which is given by the formula:

(n-1)S²/χ²α/2, n-1) < σ² < (n-1)S²/χ²1-α/2, n-1)

Where S² is the sample variance.

χ²α/2, n-1) is the chi-square value for α/2 significance level and n-1 degrees of freedom.

χ²1-α/2, n-1) is the chi-square value for 1-α/2 significance level and n-1 degrees of freedom.

n is the sample size. Substituting the values in the formula, we get:

(n-1)S²/χ²α/2, n-1) < σ² < (n-1)S²/χ²1-α/2, n-1)(28 - 1)

(8)²/χ²0.05/2, 27) < σ² < (28 - 1) (8)²/χ²0.95/2, 27)(27)

(64)/41.4 < σ² < (27)(64)/13.84

(168.24) < σ² < 1262.74

Therefore, the 90% confidence interval for the variance is (168.24, 1262.74).

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Answer:

E

Step-by-step explanation:

28=28

14*2=28

4*28

they are both equal

The approximately 16.67 minutes of video will fit in a 128 gigabyte memory.

To calculate how many minutes of video will fit in a 128 gigabyte memory, we need to know the size of each frame. Let's assume that each frame is of equal size. First, we need to convert the memory size from gigabytes to bytes. Since 1 gigabyte is equal to 1,073,741,824 bytes, the memory size becomes:
128 gigabytes * 1,073,741,824 bytes per gigabyte = 137,438,953,472 bytes

Next, we need to calculate the size of each frame. To do this, we divide the memory size by the number of frames:
137,438,953,472 bytes / 60 frames per second = 2,290,649,224.53 bytes per frame

Now, we need to calculate how many frames we can fit in the memory. To do this, we divide the memory size by the size of each frame:
137,438,953,472 bytes / 2,290,649,224.53 bytes per frame = 60,000 frames

Since there are 60 frames per second, we can calculate the duration of the video by dividing the number of frames by 60:
60,000 frames / 60 frames per second = 1,000 seconds

Finally, we convert the duration from seconds to minutes:
1,000 seconds / 60 seconds per minute = 16.67 minutes

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Answer:1. 40 hours  2).7.3 hours, 3).$480 4).$611.4

Step-by-step explanation:

STEP 1

stating all requirements

regular hour = 40 hours  at $12  an hour

overtime = beyond  40 hours at $18 an hour

Step 2--- Solving out

1. Steve worked 40 regular time hours

2. Over time hours =Total 47.3 hours - 40 regular time hours = 7.3 hours

3. Regular time pay = Regular tmes hours x regular time pay rate

= 40 x $12 =$480

4) Steve gross pay = Regular time pay + overtime pay

                              = $480 + ( 7.3 hours x $18)

                              =$480+$131.4

                              =$611.4

Answer:

-12, -6, -4, -1, 9, 20

Step-by-step explanation:

9, -12, -4, 20 -1, -6

putting them in order from least to greatest means that negatives should go to the left (1st), largest should go to the right (last).

The number -9, -12, -4, 20, -6, -1 in the order from least to greatest is -12, -9, -6, -4, -4, -1, 20.

Given data: -9, -12, -4, 20, -6, -1

Starting from the smallest number:

-12 is the smallest number.

Next is -9, which is larger than -12 but smaller than -6.

Then comes -6, larger than -9 but smaller than -4.

After that, we have two occurrences of -4.

Following that is -1, greater than -4.

Finally, the largest number is 20.

So, the numbers in ascending order are: -12, -9, -6, -4, -4, -1, 20.

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Answer:

multiply 28 and 25 then divide the answer from 127

Since the triangles are similar thie means that:

Solving for x we have:

Therefore x=14

Divide the population standard deviation () by the square root of the sample size (n) to obtain the standard deviation of the sample mean (X).

The sample mean is normally distributed, with mean X= and standard deviation X=/n, where n is the sample size, for samples of any size taken from a population that is normally distributed.

The standard deviation of the population divided by the square root of the sample size is equal to the standard deviation of the sampling distribution of means.

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The two triangles are said to be congruent by the SSS rule if all three sides of one triangle are equal to the corresponding three sides of the second triangle.

Segments, or "triangles," are three-sided plane enclosed figures that can be classified according to their sides and angles. The typical variations include isosceles, equilateral, scalene, etc. So what exactly are congruent triangles? Triangles are said to be in congruence when all corresponding sides and interior angles are congruent (of the same length).

The triangles will be the same size and shape, but they will appear to be mirror images of one another. Simply put, objects that appear to be identical when placed over their opposites or that are Xerox copies of one another are said to be congruent.

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Answer:

3

Step-by-step explanation:

There are always three acute angles in an acute triangle. The definition of an acute triangle is that it is a triangle in which all angles are less than 90 degrees.

Hopefully this helps :)

Rational number

Answer:

It is rational, as it is both non-terminating and repeating.

hope it helps :D

The double integral ∬R (x^2 + y) dA over the annular region R is equal to zero.

To evaluate the double integral over the annular region R, we need to determine the limits of integration. The annular region is bounded by two circles: x^2 + y^2 = 1 and x^2 + y^2 = 5.

In polar coordinates, the equation of the inner circle is r = 1, and the equation of the outer circle is r = √5.

Since we are integrating over the entire region R, we can express the limits of integration as follows: θ varies from 0 to 2π, and r varies from 1 to √5.

The integrand is (x^2 + y), which can be written in polar coordinates as (r^2 * cos^2θ + r * sinθ).

When we integrate this expression over the annular region R, we find that the contribution from each infinitesimal area element cancels out, resulting in a total value of zero.

Therefore, the value of the double integral (x^2 + y) dA over the annular region R is zero.

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Answer:

Therefore, over a period of 15 years, the account balance will be higher if Johnny deposits $150 a month than if he deposits $75 a month for 30 years.

Step-by-step explanation:

Johnny should choose the option that deposits $150 a month for 15 years, because this will result in the highest account balance. This is due to the effect of compound interest; when a person invests in an account with compound interest, their balance will increase by more each period due to the interest they earn being added to their principal balance.

Therefore, over a period of 15 years, the account balance will be higher if Johnny deposits $150 a month than if he deposits $75 a month for 30 years.

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